Experiencing geometry : Euclidean and non-Euclidean with history
著者
書誌事項
Experiencing geometry : Euclidean and non-Euclidean with history
Pearson Prentice Hall, c2005
3rd ed
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注記
Includes bibliographical references (p. 375-384) and index
内容説明・目次
内容説明
For junior/senior level course in Geometry.
The distinctive approach of Henderson and Taimina's text stimulates students to develop a broader, deeper understanding of mathematics through active experience-including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting problems (ranging from easy to challenging) encourage students to gather and discuss their reasonings and understanding. This is the only undergraduate text that pays attention to geometric intuition, student cognitive development, and rigorous mathematics; and that includes a broad vision of geometry that leads to discussion of four strands in the history of geometry and to an understanding of the possible shapes of the physical universe.
目次
Preface.
How to Use this Book.
0. Historical Strands of Geometry.
1. What is Straight?
2. Straightness on Spheres.
3. What Is an Angle?
4. Straightness on Cylinders and Cones.
5. Straightness on Hyperbolic Planes.
6. Triangles and Congruencies.
7. Area and Holonomy.
8. Parallel Transport.
9. SSS, ASS, SAA, and AAA.
10. Parallel Postulates.
11. Isometries and Patterns.
12. Dissection Theory.
13. Square Roots, Pythagoras and Similar Triangles.
14. Projections of a Sphere onto a Plane.
15. Circles.
16. Inversions in Circles.
17. Projections (Models) of Hyperbolic Planes.
18. Geometric 2-Manifolds.
19. Geometric Solutions of Quadratic and Cubic Equations.
20. Trigonometry and Duality.
21. Mechanisms.
22. 3-Spheres and Hyperbolic 3-Spaces.
23. Polyhedra.
24. 3-Manifolds-the Shape of Space.
Appendix A: Euclid's Definitions, Postulates, and Common Notions.
Appendix B: Constructions of Hyperbolic Planes.
Bibliography.
Index.
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